Calls grew on Monday for an inquiry into reports that Australian officials paid people-smugglers bound for Australia thousands of dollars to turn their boat back to Indonesia, with Jakarta and the United Nations also expressing serious concern.

Australia has vowed to stop asylum-seekers reaching its shores, turning boats back to Indonesia when it can and sending asylum-seekers for long-term detention in camps in impoverished South Pacific nations Papua New Guinea and Nauru.

A boat captain and two crew members arrested last week on suspicion of human trafficking told Indonesian police Australian authorities had paid each of them A$5,000 ($3,860) to turn back their vessel with 65 migrants on board.

The passengers, including children and a pregnant woman, were from Bangladesh, Sri Lanka and Myanmar.

Australian Foreign Minister Julie Bishop and Immigration Minister Peter Dutton have both denied reports of payment to the smugglers but Prime Minister Tony Abbott has declined to comment, citing operational security.

A growing chorus of opposition politicians has called on the government to explain the allegations. Independent Senator Glenn Lazarus said Abbott should resign if they are found to be true.

On Monday, opposition Labor Party immigration spokesman Richard Marles said he had written to Australia's auditor-general seeking an inquiry.

"If this happened, there are serious questions about the legal basis upon which it has happened," Marles said.

There are signs the allegations are already straining the relations between uneasy neighbours Australia and Indonesia, which are only just beginning to improve after the execution of two Australians in Indonesia earlier this year on drugs charges.

On Saturday, Indonesian foreign ministry spokesman Armanatha Nasir said Australia would have stooped to a "new low" if the reports were true.

Bishop lashed out at Jakarta in an interview with The Australian newspaper published on Monday, placing any blame squarely on Indonesia for what she said were its lax border control measures.

"The best way for Indonesia to resolve any concerns it has ... is for Indonesia to enforce sovereignty over its borders," she said.

"Operation Sovereign Borders is necessary because Indonesian boats with Indonesian crews are leaving Indonesia with the express intention of breaching our sovereignty, facilitated by illegal people-smuggling syndicates," she said, using Australia's name for its border policing operations.

The United Nations and human rights groups have criticised Australia over its tough asylum-seeker policy, which Abbott defends as necessary to stop deaths at sea.